Answer
$-\dfrac{\sqrt[3]{2x^{4}}}{9}+\sqrt[3]{\dfrac{250x^{4}}{27}}=\dfrac{14x\sqrt[3]{2x}}{9}$
Work Step by Step
$-\dfrac{\sqrt[3]{2x^{4}}}{9}+\sqrt[3]{\dfrac{250x^{4}}{27}}$
Rewrite this expression as $\dfrac{\sqrt[3]{125\cdot2x^{4}}}{\sqrt[3]{27}}-\dfrac{\sqrt[3]{2x^{4}}}{9}$ and simplify both terms:
$-\dfrac{\sqrt[3]{2x^{4}}}{9}+\sqrt[3]{\dfrac{250x^{4}}{27}}=\dfrac{\sqrt[3]{125\cdot2x^{4}}}{\sqrt[3]{27}}-\dfrac{\sqrt[3]{2x^{4}}}{9}=...$
$...=\dfrac{5x\sqrt[3]{2x}}{3}-\dfrac{x\sqrt[3]{2x}}{9}=...$
Evaluate the substraction and simplify if possible:
$...=\Big[\dfrac{5x(3)-x}{9}\Big]\sqrt[3]{2x}=\dfrac{15x-x}{9}\sqrt[3]{2x}=\dfrac{14x\sqrt[3]{2x}}{9}$
